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Question 20, Page 234
Solution Method 1.
...............................
See Solution Method 2 at RIGHT
The time per workout an athlete uses a stairclimber is normally distributed, with a mean of
20 minutes and a standard deviation of 5 minutes.
An athlete is randomly selected.
a.
Find the probability that the athlete uses a stairclimber for less than 17 minutes.
b.
Find the probability that the athlete uses a stairclimber between 17 and 22 minutes.
c.
Find the probabiliity that the athlete uses a stairclimber for more than 22 minutes.
Solution:
First, we recall that a normal distribution extends approximately three standard
deviations above and below the mean.
Thus, the time on the stairclimber will probably be
within 3 standard deviations, or 3*5 = 15 minutes.
Thus, the possible values of time will
extend from 20 - 15 = 5 to 20 + 15 = 35.
We create a column of Minutes ranging from 5 to 35, in one minute increments.
(Use Edit
--> Fill --> Series to create the list.)
This column is shown at right.
Next, use the NORMDIST function to generate a column of Area to the Left.
This function
has the format NORMDIST(x,mean,stddev,true).
In this case, the formula for cell B12 will
look like:
=NORMDIST(A12,20,5,true)
We then add another column to covert to
percentage.
Part A:
The answer is the area to the left of 17.
This is given in the Area to the Left
column.
Thus, simply look up x = 17.
That is, P(x<17) = 0.2743 = 27.43%.
Part B:
The answer is the area between 17 and 22.
Since the table gives Area to the
Left, we look up 22 and 17, then subtract the area.
(Answer will always be positive, so be
sure to subtract smallest from largest.)
That is, P(17<x<22) = 0.6554 - 0.2743 = 0.3811 =
38.11%
Part C:
The answer is the area above 22.
Since the table gives Area to the Left (or Area
Below), we look up 22 and subtract the area from 1.
That is, P(x>22) = 1 - P(x<22) = 1 -
0.6554 = 0.3446 = 34.46%